共查询到20条相似文献,搜索用时 46 毫秒
1.
P. G. Hjorth S. L. Kokkendorff S. Markvorsen 《Proceedings of the American Mathematical Society》2002,130(1):175-181
We study finite metric spaces with elements picked from, and distances consistent with, ambient Riemannian manifolds. The concepts of negative type and strictly negative type are reviewed, and the conjecture that hyperbolic spaces are of strictly negative type is settled, in the affirmative. The technique of the proof is subsequently applied to show that every compact manifold of negative type must have trivial fundamental group, and to obtain a necessary criterion for product manifolds to be of negative type.
2.
We consider the energy (or the total bending) of unit vector fields oncompact Riemannian manifolds for which the set of its singularitiesconsists of a finite number of isolated points and a finite number ofpairwise disjoint closed submanifolds. We determine lower bounds for theenergy of such vector fields on general compact Riemannian manifolds andin particular on compact rank one symmetric spaces. For this last classof spaces, we compute explicit expressions for the total bending whenthe unit vector field is the gradient field of the distance function toa point or to special totally geodesic submanifolds (i.e., for radialunit vector fields around this point or these submanifolds). 相似文献
3.
Samuel Tebege 《Geometriae Dedicata》2007,129(1):155-171
We analyze polar actions on Hermitian and quaternion-Kähler symmetric spaces of compact type. For complex integrable polar actions on Hermitian symmetric spaces of compact type we prove a reduction theorem and several corollaries concerning the geometry of these actions. The results are independent of the classification of polar actions on Hermitian symmetric spaces. In the second part we prove that polar actions on Wolf spaces are quaternion-coisotropic and that isometric actions on these spaces admit an orbit of special type, analogous to the existence of a complex orbit for an isometric action on a compact homogeneous simply connected Kähler manifold. 相似文献
4.
The purpose of this work is to describe an abstract theory of Hardy-Sobolev spaces on doubling Riemannian manifolds via an atomic decomposition. We study the real interpolation of these spaces with Sobolev spaces and finally give applications to Riesz inequalities. 相似文献
5.
Christopher Connell 《Geometriae Dedicata》2002,93(1):205-233
Here we present a necessary and sufficient condition for a negatively curved homogeneous space to be a rank one symmetric space. In particular, we show rigidity if such a space has positive hyperbolic rank greater than equal to that of its 'Abelian direction'. The notion of hyperbolic-rank extends the notion of rank in negatively curved spaces. The central theorem is an analogue of a result by U. Hamenstädt for compact negatively curved manifolds. We also provide an example of a nonsymmetric hyperbolic rank two homogeneous space, demonstrating the sharpness of the theorem. 相似文献
6.
We study fractional Sobolev and Besov spaces on noncompact Riemannian manifolds with bounded geometry. Usually, these spaces are defined via geodesic normal coordinates which, depending on the problem at hand, may often not be the best choice. We consider a more general definition subject to different local coordinates and give sufficient conditions on the corresponding coordinates resulting in equivalent norms. Our main application is the computation of traces on submanifolds with the help of Fermi coordinates. Our results also hold for corresponding spaces defined on vector bundles of bounded geometry and, moreover, can be generalized to Triebel‐Lizorkin spaces on manifolds, improving [11]. 相似文献
7.
Robert Petit 《Annals of Global Analysis and Geometry》2009,35(1):1-37
We derive Mok-Siu-Yeung type formulas for horizontal maps from compact contact locally sub-symmetric spaces into strictly
pseudoconvex CR manifolds and we obtain some rigidity theorems for the horizontal pseudoharmonic maps.
相似文献
8.
Anna L. Mazzucato 《Transactions of the American Mathematical Society》2003,355(4):1297-1364
This paper is devoted to the analysis of function spaces modeled on Besov spaces and their applications to non-linear partial differential equations, with emphasis on the incompressible, isotropic Navier-Stokes system and semi-linear heat equations. Specifically, we consider the class, introduced by Hideo Kozono and Masao Yamazaki, of Besov spaces based on Morrey spaces, which we call Besov-Morrey or BM spaces. We obtain equivalent representations in terms of the Weierstrass semigroup and wavelets, and various embeddings in classical spaces. We then establish pseudo-differential and para-differential estimates. Our results cover non-regular and exotic symbols. Although the heat semigroup is not strongly continuous on Morrey spaces, we show that its action defines an equivalent norm. In particular, homogeneous BM spaces belong to a larger class constructed by Grzegorz Karch to analyze scaling in parabolic equations. We compare Karch's results with those of Kozono and Yamazaki and generalize them by obtaining short-time existence and uniqueness of solutions for arbitrary data with subcritical regularity. We exploit pseudo-differential calculus to extend the analysis to compact, smooth, boundaryless, Riemannian manifolds. BM spaces are defined by means of partitions of unity and coordinate patches, and intrinsically in terms of functions of the Laplace operator.
9.
Vector cross product structures on manifolds include symplectic, volume, G2- and Spin(7)-structures. We show that the knot spaces of such manifolds have natural symplectic structures, and relate instantons and branes in these manifolds to holomorphic disks and Lagrangian submanifolds in their knot spaces.For the complex case, the holomorphic volume form on a Calabi-Yau manifold defines a complex vector cross product structure. We show that its isotropic knot space admits a natural holomorphic symplectic structure. We also relate the Calabi-Yau geometry of the manifold to the holomorphic symplectic geometry of its isotropic knot space. 相似文献
10.
Fabrice Baudoin 《Bulletin des Sciences Mathématiques》2002,126(6):481-491
We show that the only compact simply connected manifolds for which the radial part of Brownian motion enjoys the Markov property are compact two points homogeneous spaces, i.e. rank one symmetric spaces. 相似文献
11.
In this paper we consider transitive actions of Lie groups on analytic manifolds. We study three cases of analytic manifolds
and their corresponding transformation groups. Given a free action on the left, we define left orbit spaces and consider actions
on the right by maximal compact subgroups. We show that these actions are transitive and find the corresponding isotropy subgroups.
Further, we show that the left orbit spaces are reductive homogeneous spaces. This article thus forms the basis of a forthcoming
paper on invariant differential operators on homogeneous manifolds.
Partially supported by a Carver Research Initiative Grant. 相似文献
12.
In this paper, we construct two-step nilpotent Lie groups from homogeneous fiber bundles over compact symmetric spaces. The structure of the constructed nilpotent groups is expressed in terms of the compact Lie groups involved in the fiber bundles. There are close relations between the geometric properties of the nilpotent groups and the total spaces of the fiber bundles. We will find new examples of nilpotent groups which are weakly symmetric and Riemannian geodesic orbit spaces. 相似文献
13.
《Differential Geometry and its Applications》1999,10(2):107-119
We characterize conformally flat spaces as the only compact self-dual manifolds which are U(1)-equivariantly and conformally decomposable into two complete self-dual Einstein manifolds with common conformal infinity. A geometric characterization of such conformally flat spaces is also given. 相似文献
14.
本文利用极大点空间的等价刻划证明了极大点空间的某些子空间、不交和、 乘积空间、逆序列的逆极限、具有可数基的局部紧的Hausdorff空间是极大点空间,还 给出了具有可数基的局部紧的Hausdorff空间的Domain hull. 相似文献
15.
Let S=G/K be a strongly irreducible, simply connected, compact symmetric space and let
be its group of isometries. We classify the symmetric spaces among these that admit free, isometric circle actions. The existence of such actions is important in constructing examples of manifolds with positive sectional curvature. 相似文献
16.
主要讨论了Cn中单位球上Dirichlet型空间Dp到μ-Bloch空间βμ的加权Cesàro算子Tg的有界性和紧性问题,给出了Tg为Dp到βμ有界算子或紧算子的充要条件. 相似文献
17.
Harold Donnelly 《Geometriae Dedicata》2002,91(1):1-6
Existence and uniqueness is proved for asymptotic Dirichlet problems on Hadamard manifolds. This includes manifolds of bounded negative curvature and symmetric spaces of higher rank. 相似文献
18.
Manfredo P. do Carmo Qiaoling Wang Changyu Xia 《Annali di Matematica Pura ed Applicata》2010,189(4):643-660
In this paper, we study eigenvalues of elliptic operators in divergence form on compact Riemannian manifolds with boundary
(possibly empty) and obtain a general inequality for them. By using this inequality, we prove universal inequalities for eigenvalues
of elliptic operators in divergence form on compact domains of complete submanifolds in a Euclidean space, and of complete
manifolds admitting special functions which include the Hadamard manifolds with Ricci curvature bounded below, a class of
warped product manifolds, the product of Euclidean spaces with any complete manifold and manifolds admitting eigenmaps to
a sphere. 相似文献
19.
We prove a general embedding theorem for Sobolev spaces on open manifolds of bounded geometry and infer from this the module structure theorem. Thereafter we apply this to weighted Sobolev spaces. 相似文献